Implement ordering with dependency constraints
Problem Description
You are given n items, labeled from 0 to n-1. You are also provided with a list of precedence constraints, edges, where each edges[i] = [u, v] signifies that item u must appear before item v in any valid ordering.
Your task is to return a valid ordering of all n items that satisfies every given constraint.
Specific Requirements:
- If multiple valid orderings exist, you must return the lexicographically smallest ordering by item ID.
- If the given constraints lead to a cycle (making a valid ordering impossible), you must return the string "IMPOSSIBLE".
- You must analyze the time and space complexity of your solution.
- You must provide working code.
Follow-up: Grouping Constraints
Extend your solution to support "groups" where certain items must appear as contiguous blocks within the final ordering.
- Respect both intra-group dependencies (dependencies between items within the same group) and inter-group dependencies (dependencies between items in different groups or between a grouped item and an ungrouped item).
- For this follow-up, you may return any valid sequence (the lexicographical smallest requirement is relaxed).
- If a valid sequence is impossible due to cycles, return "IMPOSSIBLE".
AI interview prep
Core dilemma
The core dilemma is balancing the need to find *any* valid topological ordering with the specific requirement to find the *lexicographically smallest* one, all while efficiently detecting cycles and then extending this concept to handle complex "contiguous block" grouping constraints.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Implement ordering with dependency constraints
Problem Description
You are given n items, labeled from 0 to n-1. You are also provided with a list of precedence constraints, edges, where each edges[i] = [u, v] signifies that item u must appear before item v in any valid ordering.
Your task is to return a valid ordering of all n items that satisfies every given constraint.
Specific Requirements:
- If multiple valid orderings exist, you must return the lexicographically smallest ordering by item ID.
- If the given constraints lead to a cycle (making a valid ordering impossible), you must return the string "IMPOSSIBLE".
- You must analyze the time and space complexity of your solution.
- You must provide working code.
Follow-up: Grouping Constraints
Extend your solution to support "groups" where certain items must appear as contiguous blocks within the final ordering.
- Respect both intra-group dependencies (dependencies between items within the same group) and inter-group dependencies (dependencies between items in different groups or between a grouped item and an ungrouped item).
- For this follow-up, you may return any valid sequence (the lexicographical smallest requirement is relaxed).
- If a valid sequence is impossible due to cycles, return "IMPOSSIBLE".